diff --git a/pandas/core/resample.py b/pandas/core/resample.py
index b3e86b4360d74..39b2f4336730d 100644
--- a/pandas/core/resample.py
+++ b/pandas/core/resample.py
@@ -2784,7 +2784,13 @@ def asfreq(
             how = "E"
 
         if isinstance(freq, BaseOffset):
-            freq = freq_to_period_freqstr(freq.n, freq.name)
+            if hasattr(freq, "_period_dtype_code"):
+                freq = freq_to_period_freqstr(freq.n, freq.name)
+            else:
+                raise ValueError(
+                    f"Invalid offset: '{freq.base}' for converting time series "
+                    f"with PeriodIndex."
+                )
 
         new_obj = obj.copy()
         new_obj.index = obj.index.asfreq(freq, how=how)
diff --git a/pandas/tests/resample/test_period_index.py b/pandas/tests/resample/test_period_index.py
index 60b222179ba12..703abbca91d64 100644
--- a/pandas/tests/resample/test_period_index.py
+++ b/pandas/tests/resample/test_period_index.py
@@ -970,6 +970,22 @@ def test_resample_t_l_deprecated(self):
             result = ser.resample("T").mean()
         tm.assert_series_equal(result, expected)
 
+    @pytest.mark.parametrize(
+        "offset",
+        [
+            offsets.MonthBegin(),
+            offsets.BYearBegin(2),
+            offsets.BusinessHour(2),
+        ],
+    )
+    def test_asfreq_invalid_period_freq(self, offset, series_and_frame):
+        # GH#9586
+        msg = f"Invalid offset: '{offset.base}' for converting time series "
+
+        df = series_and_frame
+        with pytest.raises(ValueError, match=msg):
+            df.asfreq(freq=offset)
+
 
 @pytest.mark.parametrize(
     "freq,freq_depr",